Bounds for D-Algebraic Closure Properties

TL;DR

This paper establishes bounds on the degree of polynomial differential equations resulting from closure properties of D-algebraic functions, under certain technical conditions, complementing existing bounds on their order.

Contribution

It introduces bounds on the degree of these equations, which were previously less understood compared to order bounds, under specific technical assumptions.

Findings

Bounds on the degree of polynomial differential equations for D-algebraic functions.

Applicable under certain technical conditions on the defining differential equations.

Enhances understanding of the complexity of closure properties in D-algebraic functions.

Abstract

We provide bounds on the size of polynomial differential equations obtained by executing closure properties for D-algebraic functions. While it is easy to obtain bounds on the order of these equations, it requires some more work to derive bounds on their degree. Here we give bounds that apply under some technical condition about the defining differential equations.